(>>=) creates extra events?

Questions and Answers
1

I was surprised by this behaviour of (>>=):

this should be a stream of "note 0", at 1/2, 3/2, 5/2, etc?

d1 $ pure 0 >>= \ _ ->
    ( (1/2) ~> (s "superpiano" + note 0  ))

But it's not, events are at 0, 1/2, 1, 3/2, 2, 5/2, ...

By the Monad law pure x >>= f = f x, it should be equivalent to

d1 $ ( (1/2) ~> (s "superpiano" + note 0  ))

which gives the expected result.

test case without audio:

ghci> pure  () >>= \ _ -> rotR (1/2) (  pure () )
(0>½)|()
(½>1)|()

ghci>  rotR (1/2) (  pure () )
-1½-(0>½)|()
 (½>1)-1½|()

ghci> tidal_version 
"1.9.5"

it's not primarily about monads - my application was an offbeat chord in a reggae, where the pattern before (>>=) gives the base note.

2

Ah, now I see - I want the monadic bind via innerJoin, while current (>>=) uses unwrap.

ghci> (\ p f -> unwrap (fmap f p)) ( pure  () ) ( \ _ -> rotR (1/2) (  pure () ) )
(0>½)|()
(½>1)|()

ghci> (\ p f -> innerJoin (fmap f p)) ( pure  () ) ( \ _ -> rotR (1/2) (  pure () ) )
-1½-(0>½)|()
 (½>1)-1½|()

ghci> rotR (1/2) (  pure () ) 
-1½-(0>½)|()
 (½>1)-1½|()

just by grepping and counting, it seems to me that innerJoin is used much more often than unwrap. Perhaps the observation in my question is the reason?

NB - previous discussion (of monadic bind and laws) Instance Monad Pattern should use squeezeJoin instead of unwrap? ... and the current observation is " should use innerJoin"?

[EDIT] here is another example for innerJoin $ fmap .. (that is, >>=) Using dynamic values inside within or whenT - #2 by yaxu